Pub Date : 2022-12-12DOI: 10.33581/1561-4085-2022-25-4-341-348
O. Romanov, I. Timoshchenko
The paper describes methods for theoretical and numerical simulation of the photoacoustic effect that occurs in one-dimensional carbon micro- and nanostructures under an action of pulsed laser radiation. The proposed numerical modeling technique is based on solving the equations of motion of continuous media in the Lagrange form for spatially inhomogeneous media. This model makes it possible to calculate fields of temperature, pressure, density, and velocity of the medium depending on the parameters of laser pulses and characteristics of micro- and nanostructures.
{"title":"Numerical Simulation of Photoacoustic Effect in One-Dimensional Carbon Nanostructures","authors":"O. Romanov, I. Timoshchenko","doi":"10.33581/1561-4085-2022-25-4-341-348","DOIUrl":"https://doi.org/10.33581/1561-4085-2022-25-4-341-348","url":null,"abstract":"The paper describes methods for theoretical and numerical simulation of the photoacoustic effect that occurs in one-dimensional carbon micro- and nanostructures under an action of pulsed laser radiation. The proposed numerical modeling technique is based on solving the equations of motion of continuous media in the Lagrange form for spatially inhomogeneous media. This model makes it possible to calculate fields of temperature, pressure, density, and velocity of the medium depending on the parameters of laser pulses and characteristics of micro- and nanostructures.","PeriodicalId":43601,"journal":{"name":"Nonlinear Phenomena in Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44698276","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-12DOI: 10.33581/1561-4085-2022-25-4-405-412
A. Zherelo, S. Chernogorskiy, K. Shvetsov
In this paper we use various methods of modeling of random processes to research the stochastic modification of the model of the controlled sustainable development of the region. Numerical experiments were carried out for the proposed model. The experimental results indicate a significant influence of randomness on the behavior of the system.
{"title":"On One Approach to Mathematical Modeling of Socio-EconomicDevelopment of Regions","authors":"A. Zherelo, S. Chernogorskiy, K. Shvetsov","doi":"10.33581/1561-4085-2022-25-4-405-412","DOIUrl":"https://doi.org/10.33581/1561-4085-2022-25-4-405-412","url":null,"abstract":"In this paper we use various methods of modeling of random processes to research the stochastic modification of the model of the controlled sustainable development of the region. Numerical experiments were carried out for the proposed model. The experimental results indicate a significant influence of randomness on the behavior of the system.","PeriodicalId":43601,"journal":{"name":"Nonlinear Phenomena in Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41902742","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-12DOI: 10.33581/1561-4085-2022-25-4-377-380
S. A. Kashchenko, A. Tolbey
Asymptotic methods are used to study solutions of a modified logistic equation with a delay containing a large parameter. A result on the existence and stability of a relaxation cycle is given.
{"title":"Relaxation Cycles in the Generalized Logistic Equation with Delay","authors":"S. A. Kashchenko, A. Tolbey","doi":"10.33581/1561-4085-2022-25-4-377-380","DOIUrl":"https://doi.org/10.33581/1561-4085-2022-25-4-377-380","url":null,"abstract":"Asymptotic methods are used to study solutions of a modified logistic equation with a delay containing a large parameter. A result on the existence and stability of a relaxation cycle is given.","PeriodicalId":43601,"journal":{"name":"Nonlinear Phenomena in Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47795616","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-12DOI: 10.33581/1561-4085-2022-25-4-318-325
I. A. Serenkova, A. Pankov, V. Bednyakov
The expected ATLAS Run 3 data set with time-integrated luminosity of 300 fb−1 and HL–LHC options at the LHC in the diboson channels are used to probe a simple benchmark model with an extended gauge sector, proposed by Altarelli et al. This model accommodates new charged W' and neutral Z' vector bosons with modified trilinear Standard Model gauge couplings, decaying into electroweak gauge boson pairs W Z or W W, where W / Z decay semileptonically. Also presented, from a similar analysis of W' and Z' bosons arising in the EGM, which can decay through W' → lν and Z' → ll , are limits on the W–W' and Z–Z' mixing parameters and the W' and Z' vector boson masses. We present upper limits on the mixing parameters, Z–Z' and W–W', by using the expected Run 3 data and HL–LHC options.
{"title":"Improved Constraints on the Heavy Gauge Bosons Decaying to Pairs of Electroweak Bosons by Using the Expected Run 3 Data and HL-LHC Options","authors":"I. A. Serenkova, A. Pankov, V. Bednyakov","doi":"10.33581/1561-4085-2022-25-4-318-325","DOIUrl":"https://doi.org/10.33581/1561-4085-2022-25-4-318-325","url":null,"abstract":"The expected ATLAS Run 3 data set with time-integrated luminosity of 300 fb−1 and HL–LHC options at the LHC in the diboson channels are used to probe a simple benchmark model with an extended gauge sector, proposed by Altarelli et al. This model accommodates new charged W' and neutral Z' vector bosons with modified trilinear Standard Model gauge couplings, decaying into electroweak gauge boson pairs W Z or W W, where W / Z decay semileptonically. Also presented, from a similar analysis of W' and Z' bosons arising in the EGM, which can decay through W' → lν and Z' → ll , are limits on the W–W' and Z–Z' mixing parameters and the W' and Z' vector boson masses. We present upper limits on the mixing parameters, Z–Z' and W–W', by using the expected Run 3 data and HL–LHC options.","PeriodicalId":43601,"journal":{"name":"Nonlinear Phenomena in Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41826969","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-12DOI: 10.33581/1561-4085-2022-25-4-387-404
E. Ovsiyuk, O. Semenyuk, A. Ivashkevich, M. Neagu
We start with the Stuckelberg tensor system of equations for a boson with spin states S = 1 and S = 0 and fixed intrinsic parity, which is transformed to the matrix form, then generalize this matrix system to the generally covariant case with the use of the tetrad method. This equation is detailed in spherical coordinates in the presence of an external Coulomb field. After separation of the variables we derive the system of 11 radial equations. By diagonalizing the space reflection operator, this system is splitted into two system of four and seven equations for the states with the parities P = (−1) j+1 and P = (−1) j respectively. The system for the states with the parities P = (−1) j+1 leads to the known solution and energy spectrum. The system of seven equations for the states with the parities P = (−1) j is solved for the states with the total angular momentum j = 0 in terms of hypergeometric functions. The system of seven equations for the states with the total angular momenta j = 1, 2, 3, ... turns out to be very complicated, the only nonrelativistic approximation has been studied. The derived nonrelativistic equations are solved in terms of confluent hypergeometric functions, and the corresponding energy spectra are found. In addition, the general form of the nonrelativistic equations for the the Stuckelberg particle is derived in the presence of an arbitrary electromagnetic field.
{"title":"Stuckelberg Particle in a Coulomb Field: A Non-Relativistic Approximation","authors":"E. Ovsiyuk, O. Semenyuk, A. Ivashkevich, M. Neagu","doi":"10.33581/1561-4085-2022-25-4-387-404","DOIUrl":"https://doi.org/10.33581/1561-4085-2022-25-4-387-404","url":null,"abstract":"We start with the Stuckelberg tensor system of equations for a boson with spin states S = 1 and S = 0 and fixed intrinsic parity, which is transformed to the matrix form, then generalize this matrix system to the generally covariant case with the use of the tetrad method. This equation is detailed in spherical coordinates in the presence of an external Coulomb field. After separation of the variables we derive the system of 11 radial equations. By diagonalizing the space reflection operator, this system is splitted into two system of four and seven equations for the states with the parities P = (−1) j+1 and P = (−1) j respectively. The system for the states with the parities P = (−1) j+1 leads to the known solution and energy spectrum. The system of seven equations for the states with the parities P = (−1) j is solved for the states with the total angular momentum j = 0 in terms of hypergeometric functions. The system of seven equations for the states with the total angular momenta j = 1, 2, 3, ... turns out to be very complicated, the only nonrelativistic approximation has been studied. The derived nonrelativistic equations are solved in terms of confluent hypergeometric functions, and the corresponding energy spectra are found. In addition, the general form of the nonrelativistic equations for the the Stuckelberg particle is derived in the presence of an arbitrary electromagnetic field.","PeriodicalId":43601,"journal":{"name":"Nonlinear Phenomena in Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42583737","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-12DOI: 10.33581/1561-4085-2022-25-4-312-317
H. Terazawa
In the unified subquark model of all fundamental particles and forces, the mass of the Higgs boson in the standard model of electroweak interactions (mH) is predicted to be about 2√6 mW / 3 (where mW is the mass of the charged weak boson, W ), which agrees well with the experimental values of about 125 GeV found by the ATLAS and CMS Collaborations at the LHC in 2011. It seems to indicate that the Higgs boson is a composite of the iso-doublet spinor subquark-antisubquark pairs well described by the unified subquark model with either one of subquark masses vanishing or being very small compared to the other. In the unified composite model, there may appear a daughter of the Higgs boson whose mass is predicted to be 2 mW /√3, which agrees well with the experimental values of about 95 GeV for the excess events, found by the LEP experiments and recently by the CMS experiment. This agreement seems to strongly indicate not only the compositeness of the Higgs bosons but also the validity of the unified composite model of all fundamental particles and forces.
{"title":"Daughter Higgs Boson in the Unified Composite Model","authors":"H. Terazawa","doi":"10.33581/1561-4085-2022-25-4-312-317","DOIUrl":"https://doi.org/10.33581/1561-4085-2022-25-4-312-317","url":null,"abstract":"In the unified subquark model of all fundamental particles and forces, the mass of the Higgs boson in the standard model of electroweak interactions (mH) is predicted to be about 2√6 mW / 3 (where mW is the mass of the charged weak boson, W ), which agrees well with the experimental values of about 125 GeV found by the ATLAS and CMS Collaborations at the LHC in 2011. It seems to indicate that the Higgs boson is a composite of the iso-doublet spinor subquark-antisubquark pairs well described by the unified subquark model with either one of subquark masses vanishing or being very small compared to the other. In the unified composite model, there may appear a daughter of the Higgs boson whose mass is predicted to be 2 mW /√3, which agrees well with the experimental values of about 95 GeV for the excess events, found by the LEP experiments and recently by the CMS experiment. This agreement seems to strongly indicate not only the compositeness of the Higgs bosons but also the validity of the unified composite model of all fundamental particles and forces.","PeriodicalId":43601,"journal":{"name":"Nonlinear Phenomena in Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42551477","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-12DOI: 10.33581/1561-4085-2022-25-4-336-340
Á. Baran, V. Kudryashov
Energy levels of electrons in semiconductor quantum dots are obtained within the framework of perturbation theory taking into account the Rashba and Dresselhaus spin-orbit interactions and an external magnetic field. The circular quantum dots are simulated by a new smooth confinement potential of a finite depth and width. The dependence of energy levels on a constant uniform magnetic field and potential parameters is presented.
{"title":"Influence of Magnetic Field on Electron Energy Levels in Semconductor Quantum Dots in the Presence of Spin-Orbit Interactions","authors":"Á. Baran, V. Kudryashov","doi":"10.33581/1561-4085-2022-25-4-336-340","DOIUrl":"https://doi.org/10.33581/1561-4085-2022-25-4-336-340","url":null,"abstract":"Energy levels of electrons in semiconductor quantum dots are obtained within the framework of perturbation theory taking into account the Rashba and Dresselhaus spin-orbit interactions and an external magnetic field. The circular quantum dots are simulated by a new smooth confinement potential of a finite depth and width. The dependence of energy levels on a constant uniform magnetic field and potential parameters is presented.","PeriodicalId":43601,"journal":{"name":"Nonlinear Phenomena in Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45044944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-12DOI: 10.33581/1561-4085-2022-25-4-349-358
I. V. Shapochkina, V. M. Rozenbaum
We consider the adiabatic mode of Brownian particle motion in a periodic potential under the action of symmetric dichotomous fluctuations of an external force F with zero mean value (rocking ratchet), in which the fluctuation frequency is much less than the inverse relaxation time of the particle in each of the states of the dichotomous process. Expressions are given for force-dependent fluxes of an adiabatic classical rocking ratchet. In the absence of thermal fluctuations, within the semiclassical approximation, analytical expressions are obtained for the rocking-ratchet tunneling flux in a sawtooth periodic potential of arbitrary asymmetry and in the potential of two sinusoids. It is shown that the tunneling flux has a linear asymptotics in modulus of small F due to (i) the absence of reverse tunneling fluxes with respect to the direction F and (ii) the root dependence of the integrand of the Gamow formula on the potential energy. The main parameters of the model are the energy barrier V0 and the period L of the potentials, as well as the rocking force F and the asymmetry parameter ξ = l / L of the sawtooth potential with the width of one of its teeth equal to l. It is shown that the direction of quantum ratchet motion is opposite to the motion direction of the corresponding classical ratchet in a limited range of values of the rocking force |F| L / V0 < αc , where the parameter αc changes from the value α1 = (√5 − 1) / 2 ≈ 0.618 for the extremely asymmetric sawtooth potential (ξ = 1) to the value α2 = 2 / 3 ≈ 0.667 for the symmetric potential (ξ= 1 / 2). In the range of values α2 < αc < α2, the sign of the tunneling flux changes with the change in the asymmetry parameter ξ. Numerical calculations for the potential of two sinusoids corresponding to the effective value ξ ≈ 0.655 of the asymmetry lead to similar results with αc ≈ 0.81.
{"title":"Force-dependent Fluxes of Adiabatic Classical and Quantum Rocking Ratchets","authors":"I. V. Shapochkina, V. M. Rozenbaum","doi":"10.33581/1561-4085-2022-25-4-349-358","DOIUrl":"https://doi.org/10.33581/1561-4085-2022-25-4-349-358","url":null,"abstract":"We consider the adiabatic mode of Brownian particle motion in a periodic potential under the action of symmetric dichotomous fluctuations of an external force F with zero mean value (rocking ratchet), in which the fluctuation frequency is much less than the inverse relaxation time of the particle in each of the states of the dichotomous process. Expressions are given for force-dependent fluxes of an adiabatic classical rocking ratchet. In the absence of thermal fluctuations, within the semiclassical approximation, analytical expressions are obtained for the rocking-ratchet tunneling flux in a sawtooth periodic potential of arbitrary asymmetry and in the potential of two sinusoids. It is shown that the tunneling flux has a linear asymptotics in modulus of small F due to (i) the absence of reverse tunneling fluxes with respect to the direction F and (ii) the root dependence of the integrand of the Gamow formula on the potential energy. The main parameters of the model are the energy barrier V0 and the period L of the potentials, as well as the rocking force F and the asymmetry parameter ξ = l / L of the sawtooth potential with the width of one of its teeth equal to l. It is shown that the direction of quantum ratchet motion is opposite to the motion direction of the corresponding classical ratchet in a limited range of values of the rocking force |F| L / V0 < αc , where the parameter αc changes from the value α1 = (√5 − 1) / 2 ≈ 0.618 for the extremely asymmetric sawtooth potential (ξ = 1) to the value α2 = 2 / 3 ≈ 0.667 for the symmetric potential (ξ= 1 / 2). In the range of values α2 < αc < α2, the sign of the tunneling flux changes with the change in the asymmetry parameter ξ. Numerical calculations for the potential of two sinusoids corresponding to the effective value ξ ≈ 0.655 of the asymmetry lead to similar results with αc ≈ 0.81.","PeriodicalId":43601,"journal":{"name":"Nonlinear Phenomena in Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43841747","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-12DOI: 10.33581/1561-4085-2022-25-4-368-376
V. S. Otchik
Solutions of the spin-weighted spheroidal differential equation are presented in the form of the series involving confluent hypergeometric functions. Relations between solutions with different domains of convergence are derived by considering the confluence of two singularities in an auxiliary equation with four regular singularities. These relations are used to obtain exponentially small corrections to asymptotic expansion of eigenvalues.
{"title":"On the Asymptotics of Eigenvalues of the Spin-Weighted Spheroidal Equation","authors":"V. S. Otchik","doi":"10.33581/1561-4085-2022-25-4-368-376","DOIUrl":"https://doi.org/10.33581/1561-4085-2022-25-4-368-376","url":null,"abstract":"Solutions of the spin-weighted spheroidal differential equation are presented in the form of the series involving confluent hypergeometric functions. Relations between solutions with different domains of convergence are derived by considering the confluence of two singularities in an auxiliary equation with four regular singularities. These relations are used to obtain exponentially small corrections to asymptotic expansion of eigenvalues.","PeriodicalId":43601,"journal":{"name":"Nonlinear Phenomena in Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45691011","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-12DOI: 10.33581/1561-4085-2022-25-4-359-367
S. Sytova
The article is devoted to overview of different types of vacuum electronic devices with two or more charged particle beams. There are travelling wave and backward wave tubes, free electron lasers and masers, volume free electron lasers. Two different cases take place in such situation: multiple-beam instability in such devices and multiple-stream instability. In the first case some charged particle beams moves in the system with different velocities. In the second one there are beams with almost equal velocities (streams). Two systems of equations for volume free electron laser with two electron beams are proposed. Some numerical results of VFEL numerical simulation are given and discussed.
{"title":"Nonlinear Dynamics of Radiation in Multiple-Beam Vacuum Electronic Devices","authors":"S. Sytova","doi":"10.33581/1561-4085-2022-25-4-359-367","DOIUrl":"https://doi.org/10.33581/1561-4085-2022-25-4-359-367","url":null,"abstract":"The article is devoted to overview of different types of vacuum electronic devices with two or more charged particle beams. There are travelling wave and backward wave tubes, free electron lasers and masers, volume free electron lasers. Two different cases take place in such situation: multiple-beam instability in such devices and multiple-stream instability. In the first case some charged particle beams moves in the system with different velocities. In the second one there are beams with almost equal velocities (streams). Two systems of equations for volume free electron laser with two electron beams are proposed. Some numerical results of VFEL numerical simulation are given and discussed.","PeriodicalId":43601,"journal":{"name":"Nonlinear Phenomena in Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44906271","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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